I’m about to laud the New York Times Sunday Crossword (link to paywall), “Mirror Reflection” by Derrick Niederman, for its cleverness. I am not going to spoil any answers, but I am going to spoil the clues. Except that I’m not going to say anything that you would not figure out immediately simply by reading the clues themselves. No figuring required.

Nevertheless, you might want to avoid the spoiler if you are planning on doing the puzzle.

The Across definitions for mirrored positions are exactly the same, but the answers are different. E.g., the clue for the word in the upper left corner is “One of the blanks in the cereal slogan ‘___ are for ___'”. That’s exactly the same clue for the word in the lower right corner.

I gave that example because those two positions are the easiest to describe, but it is actually one of the weaker clues. Many of them are quite clever. I haven’t finished it yet, so there may be some that are irritating, but the design of the puzzle is audacious.

And now for extra credit, within an order of magnitude, how many people subscribe to the online version of the Boston Globe? Hint: It costs $3.99/week. Hint: Greater Boston’s population is about 4M. Hint: This quarter, online subscriptions rose 8%. (The answer comes from an article at BizOnline.)

28,000

By the way, I occasionally like to acknowledge that the “order of magnitude puzzle” was invented by my famous friend Paul English.

In analog days, the shutter let light in for some determinant time. That caused the film to be exposed for that duration. But in the digital age, why doesn’t “setting the shutter speed” just tell the internal computer how long it should record data from the sensor? What good does it do to actually open and close a physical shutter?

One of the security options with Android lets you sign in by dragging you finger to trace a pattern you’ve chosen on a 3×3 square numbered 1-9. The codes have to be at least 4 digits long, you can’t repeat any digit, and you can’t lift your finger off the pad. To my always-wrong intuition, that seems like it affords too few possibilities. So, your task is to guess (or, if you must, figure out) roughly how many choices there are.

[Semi-Spoilers] You start with with the following range of numbers: 1,234 to 987,654,321. That is a boatload of numbers. But you remove all the numbers that have repeated digits. For a 9-digit number, there are only 362,880 numbers (9 factorial) without repeated digits, so that’s like subtracting 100 million numbers from the mix. Our son Nathan says that it’s the same number for all the 8-digit possibilities, because 8 factorial x 9 is the same same as 9 factorial. (I’m lost. Ask him.) After you do all of them down through 4-digits, you have to subtract the sequences that have non-contiguous numbers (based on the 3×3 square). So, it’s a big number, especially since the Android UI puts in a time-out after 10 wrong tries. But it’s not an astronomical number. I’m guessing it’s under a million.

My understanding (possibly bogus) is that moths spiral into flames because evolution has designed them to fly in straight lines by noting celestial lights. When the light is nearby, keeping its position fixed in their visual space causes them to spiral inward toward it.

Fine. But why is it an evolutionary advantage for moths to fly in a straight line? Where are they trying to get to so quickly? And isn’t there a metaphor for MBAs somewhere in here?

The following is an Order of Magnitude puzzle: Guess within an order of magnitude of the answer and you win! You win nothing!

If you were to start any spot on land on Earth and dig a hole through the center of the Earth, what percent of the time would you come out on another spot on land, as opposed to having water spray out, comically spinning the Earth out of orbit to its death? (To be precise, the question isn’t about water spraying or not spraying out of the hole. It’s about the percentage of times you’d hit land.)

The answer is in the comments. But, wait, to help you, this fabulous mashup using the Google Maps API will let you sink your own knitting needles through the Earth’s nougaty core!

(All of this came from a mailing list I’m not supposed to acknowledge. Answers authenticated by the good folks at Wikipedia.)